Anthony Gruppuso/US PresswireNew Net Shawne Williams (left) resurrected his career last season when he played for the Knicks.

The Knicks really wanted Shawne Williams. In the end, though, they didn’t have what it took to get him: money.

All the Knicks had to offer Williams — who resurrected his career with them last season, when he averaged 7.1 points and 3.7 rebounds and shot 40.1 percent from 3-point range — was the mini mid-level exception, $2.5 million per year. The Nets, coming into the picture late, offered him a lot more than that.

“But I want to thank the Knicks organization — everybody that gave me a chance over there. It was a hard decision to make, but I feel like I made the right decision. I did it for me, my family and my career, basically.”

Williams will be able to thank many of those Knicks people in person Saturday at Prudential Center, when the Nets play host to the Knicks in the first of two preseason games for the teams. According to Nets coach Avery Johnson, the 6-9 Williams won’t start Saturday, but could see some action in the game. Apparently, he showed up to camp in decent shape.

“The way he looked today I’d sure like to get him a few minutes, just to get him out there,” Johnson said.

Williams is in his second stint with the Nets. His first go-around didn’t last very long, though. The former first-round draft pick (2006, by Indiana) had been traded to the Nets as a throw-in with Kris Humphries in the Eduardo Najera deal in January 2010, but was cut four days later after news broke that he’d been arrested in his native Memphis on a drug charge. He pleaded guilty to that charge and served six months probation.

In July 2010, Williams was arrested again, this time for driving with a suspended license. Former college teammate Kareem Cooper was in the car with him, and found in possession of a gun and marijuana.

The Knicks, though, signed Williams as a free agent before last season and it paid off for the team as well as reviving the 25-year-old’s career.

Nets GM Billy King, asked about Williams’ checkered history, said he did “take that into consideration” but said he believed the Nets could “put a good support system around him.”

“I think he proved it last year, that he’s on the right track,” King said. “I look at this situation — he’s got a fresh start, to try and play with one of the best point guards (and) get some wide-open looks.”

That point guard, Deron Williams, encouraged King to sign Shawne Williams, he said Thursday. And after seeing him practice today, Deron Williams liked what he saw.

“He looked good,” Deron Williams said. “He looks to be in shape; he can shoot the ball. He’s a smart kid, too, so he’s picking up on things pretty fast.”